Yes, there are usually over 100 players on the US server. Also, on the 18th of May the iPad version will be released which will be cross-platform compatible with the PC version. So expect many more players soon.

Like already said the answer completely depends on the definition of "a lot". When someone asked is RO2 dead there were people saying yes since there are only 1 - 1,5 thousand people playing at a time. This game has maybe 50 - 250 players playing it at a time. This means that you will not be having any difficulties finding opponents to play against but you might have to play against the same person every now and then. To me this is just a positive thing since psychology plays such a big part in this game knowing your opponent just makes the match more interesting.

I used to play it until the bugs in single player such as the game locking up randomly and having it re-placing my soldiers midway through a level, not to mention the infamous final level bug, ruined it. And no patches to fix it, instead they ignore the problem and worked on the ipad version, like wtf?!?! That's the kindof ♥♥♥♥ Ubisoft does... A shame. It had potential

Currently there are about 30 to 40 players. The tournament is once per month and lasts about two to three weeks. There are players from any skill level there (from absolute beginners to people in the top 20). It's quite a lot of fun! :)

Frozen Synapse can stay healthy with a much smaller community of players than a lot of other games, since you don't even need to be online as the other guy to play. That said, there are still enough people playing that I've never noticed problems finding an opponent.